Geometric representation of interval exchange maps over algebraic number fields

We consider the restriction of interval exchange transformations to algebraic number fields, which leads to maps on lattices. We characterize renormalizability arithmetically, and study its relationships with a geometrical quantity that we call the drift vector. We exhibit some examples of renormalizable interval exchange maps with zero and non-zero drift vector, and carry out some investigations of their properties. In particular, we look for evidence of the finite decomposition property: each lattice is the union of finitely many orbits.Comment: 34 pages, 8 postscript figure

Cross sections for geodesic flows and \alpha-continued fractions

We adjust Arnoux's coding, in terms of regular continued fractions, of the geodesic flow on the modular surface to give a cross section on which the return map is a double cover of the natural extension for the \alpha-continued fractions, for each $\alpha$ in (0,1]. The argument is sufficiently robust to apply to the Rosen continued fractions and their recently introduced \alpha-variants.Comment: 20 pages, 2 figure

Triangulations and Severi varieties

We consider the problem of constructing triangulations of projective planes over Hurwitz algebras with minimal numbers of vertices. We observe that the numbers of faces of each dimension must be equal to the dimensions of certain representations of the automorphism groups of the corresponding Severi varieties. We construct a complex involving these representations, which should be considered as a geometric version of the (putative) triangulations

Observation of confined current ribbon in JET plasmas

we report the identification of a localised current structure inside the JET plasma. It is a field aligned closed helical ribbon, carrying current in the same direction as the background current profile (co-current), rotating toroidally with the ion velocity (co-rotating). It appears to be located at a flat spot in the plasma pressure profile, at the top of the pedestal. The structure appears spontaneously in low density, high rotation plasmas, and can last up to 1.4 s, a time comparable to a local resistive time. It considerably delays the appearance of the first ELM.Comment: 10 pages, 6 figure

Theory-based scaling of the SOL width in circular limited tokamak plasmas

A theory-based scaling for the characteristic length of a circular, limited tokamak scrape-off layer (SOL) is obtained by considering the balance between parallel losses and non-linearly saturated resistive ballooning mode turbulence driving anomalous perpendicular transport. The SOL size increases with plasma size, resistivity, and safety factor q. The scaling is verified against flux-driven non-linear turbulence simulations, which reveal good agreement within a wide range of dimensionless parameters, including parameters closely matching the TCV tokamak. An initial comparison of the theory against experimental data from several tokamaks also yields good agreement

Update of variants identified in the pancreatic β-cell K ATP channel genes KCNJ11 and ABCC8 in individuals with congenital hyperinsulinism and diabetes

The most common genetic cause of neonatal diabetes and hyperinsulinism is pathogenic variants in ABCC8 and KCNJ11. These genes encode the subunits of the β-cell ATP-sensitive potassium channel, a key component of the glucose-stimulated insulin secretion pathway. Mutations in the two genes cause dysregulated insulin secretion; inactivating mutations cause an oversecretion of insulin, leading to congenital hyperinsulinism, whereas activating mutations cause the opposing phenotype, diabetes. This review focuses on variants identified in ABCC8 and KCNJ11, the phenotypic spectrum and the treatment implications for individuals with pathogenic variants.This article is freely available via Open Access. Click on the publisher URL to access it via the publisher's site.P30 DK020595/NH/NIH HHS/United States K23 DK094866/NH/NIH HHS/United States R03 DK103096/NH/NIH HHS/United States 1-11-CT-41/American Diabetes Association/International R01 DK104942/DK/NIDDK NIH HHS/United States WT_/Wellcome Trust/United Kingdom WT098395/Z/12/Z/WT_/Wellcome Trust/United Kingdom UL1 TR000430/NH/NIH HHS/United States P30 DK020595/DK/NIDDK NIH HHS/United States UL1 TR000430/TR/NCATS NIH HHS/United States 1-17-JDF-008/American Diabetes Association/International 105636/Z/14/Z/WT_/Wellcome Trust/United Kingdom 110675/European Association for the Study of Diabetes-Novo Nordisk/International 16/0005407/DUK_/Diabetes UK/United Kingdom R01 DK104942/NH/NIH HHS/United States R03 DK103096/DK/NIDDK NIH HHS/United States K23 DK094866/DK/NIDDK NIH HHS/United Statespublished version, accepted version (12 month embargo), submitted versio